Uncertainty Quantification in Predicting Physical Property of Porous Medium With Bayesian Evidential Learning

The prediction of physical properties for porous medium plays an essential role in geological resource exploration and subsurface exploitation. Deterministic methods based on computational or numerical experiment provide an efficient way to estimate the physical properties of porous medium. However, uncertainty and randomness are common characteristics in the geological system. The variability of physical property in porous medium cannot be explicitly explained by a limited number of models. In this article, we propose an interval estimator-based Bayesian evidential learning (IE-BEL) framework to quantify the uncertainty while predicting physical properties of porous medium at the same time. First, we utilize a stochastic simulation to generate a number of high-quality 3-D models. Second, the morphological characteristics and physical properties are numerically computed as the training data. Third, a combination of machine learning techniques, including eXtreme gradient boosting (XGBoost) and model agnostic prediction interval estimator (MAPIE), is employed to obtain reliable interval predictions with uncertainty quantification. Fourth, a model calibration process is conducted to regulate the physical property predictions. We validate the proposed method by three practical examples, including both artificial and natural porous materials. Compared with the previous method, the IE-BEL framework shows competitive performance in predicting the physical properties of porous medium. The experiment result indicates that the proposed method can address the uncertainty quantification problem associated with physical properties prediction.